Finite Group Databasebeta

← D3×#4895 #11861023

Subgroups — D3×#4895 #11861023

Order 1152.

997 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#907C212yesmaximal, complemented
2D3×#904C211yesmaximal, characteristic
3#10592594C211yesmaximal, characteristic, complemented
4C3×#4895C211yesmaximal, characteristic, complemented
5C3×D3×#108C211yesmaximal, characteristic, complemented
6D3×#825C212yesmaximal, complemented
7#10590995C212yesmaximal, complemented
8#10590977C212yesmaximal, complemented
9#10590919C211yesmaximal, characteristic, complemented
10#10590917C211yesmaximal, characteristic, complemented
11D3×C8×Dic3C211yesmaximal, characteristic, complemented
12D3×#443—31nomaximal
13C2×#4895—31nomaximal
14D3×#235C2212yes—
15#64116C2212yescomplemented
16#64113C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×D3×M16C2212yes—
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C4×D3×Dic3C2211yescharacteristic
22#63829C2212yes—
23#63817C2212yescomplemented
24#63815C2212yescomplemented
25C2×D3×C3⋊C8C2211yescharacteristic
26#63808C411yescharacteristic, complemented
27#63807C411yescharacteristic, complemented
28#63806C412yescomplemented
29#63805—22no—
30#63804—22no—
31D3×Dic12C411yescharacteristic, complemented
32D3×D24C411yescharacteristic, complemented
33D3×#204C412yescomplemented
34D3×ΓL(1,𝔽25)—22no—
35D32×C8—22no—
36C32×#108C2211yescharacteristic, complemented
37#63652C2212yescomplemented
38C8×C3⋊Dic3C2211yescharacteristic, complemented
39C3×#825C2212yescomplemented
40C3×#822C2212yescomplemented
41C3×#819C2211yescharacteristic, complemented
42C3×C8×Dic3C2211yescharacteristic, complemented
43#63570C2212yescomplemented
44#63568C2212yescomplemented
45#63553C2211yescharacteristic, complemented
46Dic3×C3⋊C8C2211yescharacteristic, complemented
47D3×#135—31no—
48D3×#131—32no—
49C2×#907—32no—
50C2×#904—31no—
51C3×#443—31no—
52C2×C3×#108—31no—
53#5196—31no—
54#5144—32no—
55C2×#825—32no—
56C2×C8×Dic3—31no—
57#4895—32no—
58#4895—31no—
59#4895—31no—
60#4895—31no—
61#4895—32no—
62#4895—31no—
63#4895—61no—
64#4895D311yescharacteristic, direct product factor
65D3×#108D311yescharacteristic, complemented
66#4824—32no—
67D3×#104—32no—
68#4700—31no—
69C4×D3×C8—31no—
70#3828C2312yes—
71C3×#235C2312yes—
72C2×C3×C4×D3C2311yescharacteristic
73D3×#67—22no—
74#3804—22no—
75C2×D3×Dic3—21no—
76D3×D12C2×C412yes—
77C4×D32—22no—
78#3799C2×C412yes—
79#3798—22no—
80#3795C2×C412yes—
81D3×Dic6C2×C412yes—
82C32×M16C2312yes—
83C2×C32×C8C2311yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3746C2×C411yescharacteristic, complemented
87#3745C2×C411yescharacteristic, complemented
88#3744C2×C412yescomplemented
89#3743—22no—
90C8×C3⋊D3—22no—
91C3×C4×Dic3C2311yescharacteristic
92C3×#208C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12C2×C411yescharacteristic, complemented
96C3×D24C2×C411yescharacteristic, complemented
97C3×#204C2×C412yescomplemented
98C3×ΓL(1,𝔽25)—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×D3×C8—22no—
101C3×D3×C8—22no—
102C3×D3×C8C2×C411yescharacteristic
103C3×D3×C8C2×C411yescharacteristic
104C3×D3×C8C2×C411yescharacteristic
105C3×D3×C8C2×C411yescharacteristic
106Dic32—21no—
107#3719C2×C412yescomplemented
108#3717C2×C412yescomplemented
109#3716C2×C412yescomplemented
110#3714C2×C412yescomplemented
111#3712—22no—
112#3711—22no—
113#3710—22no—
114D3×C3⋊C8—22no—
115D3×C3⋊C8D411yescharacteristic
116D3×C3⋊C8D411yescharacteristic
117D3×C3⋊C8D411yescharacteristic
118D3×C3⋊C8D411yescharacteristic
119C2×#443—91noSylow
120D3×#41—32no—
121C2×#235—32no—
122C3×#135—31no—
123C3×#131—32no—
124C2×C3×M16—32no—
125C22×C3×C8—31no—
126#950—32no—
127#948—32no—
128C2×C4×Dic3—31no—
129C22×C3⋊C8—31no—
130#919—31no—
131D3×Q16—31no—
132#916—32no—
133D3×SD16—32no—
134#912—31no—
135D3×D8—31no—
136#907—32no—
137#907—32no—
138#907—32no—
139#907—32no—
140#907—62no—
141#907—62no—
142#907—62no—
143#907—62no—
144#907C2×D312yescomplemented
145D3×M16—62no—
146D3×M16C2×D312yes—
147C2×Dic12—31no—
148#904—32no—
149#904—31no—
150#904—31no—
151#904—31no—
152#904—31no—
153#904—32no—
154#904—61no—
155#904C2×D311yescharacteristic
156C2×D24—31no—
157C2×#204—32no—
158#901—32no—
159#901—62no—
160C2×ΓL(1,𝔽25)—62no—
161C2×D3×C8—31no—
162C2×D3×C8—62no—
163C2×D3×C8—62no—
164C2×D3×C8C2×D311yescharacteristic
165C42×D3—31no—
166C3×#108—21no—
167C3×#108—32no—
168C3×#108—31no—
169C3×#108C2×D311yescharacteristic, complemented
170C3×#108C2×D311yescharacteristic, complemented
171C3×#104—32no—
172C3×C4×C8—31no—
173#837—32no—
174#825—32no—
175#825—32no—
176#825—32no—
177#825—32no—
178#825—62no—
179#825C2×D312yescomplemented
180#822C2×D312yescomplemented
181#819C2×D311yescharacteristic, complemented
182C8×Dic3—31no—
183C8×Dic3—31no—
184C8×Dic3—31no—
185C8×Dic3—31no—
186C8×Dic3—31no—
187C8×Dic3—61no—
188C8×Dic3C2×D311yescharacteristic, complemented
189#805—32no—
190C4×C3⋊C8—31no—
191C22×C3×D3#4111yescharacteristic
192C2×D32—22no—
193C2×C32×C4C2411yescharacteristic
194#638—22no—
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)C22×C412yes—
197C4×C3⋊D3—22no—
198#634C22×C412yes—
199C3×#67—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3#4111yescharacteristic
202C3×D12C22×C412yes—
203C3×C4×D3—22no—
204C3×C4×D3C22×C411yescharacteristic
205C3×C4×D3C22×C411yescharacteristic
206C3×C4×D3C2×D411yescharacteristic
207C3×C4×D3C2×D411yescharacteristic
208C3×Dic6C22×C412yes—
209#627—22no—
210#626—22no—
211#626—22no—
212#625—22no—
213#624—22no—
214D3×Dic3—24no—
215D3×Dic3—22no—
216D3×Dic3—22no—
217C32×C8—22no—
218C32×C8C22×C411yescharacteristic
219C32×C8C22×C411yescharacteristic
220C3⋊(C3⋊C8)C2×D411yescharacteristic
221C3⋊(C3⋊C8)C2×D411yescharacteristic
222C3×C3⋊C8—22no—
223C3×C3⋊C8C22×C411yescharacteristic
224C3×C3⋊C8C22×C411yescharacteristic
225C3×C3⋊C8C2×D411yescharacteristic
226C3×C3⋊C8C2×D411yescharacteristic
227C2×#135—91no—
228C2×#131—92no—
229#443—31no—
230#443—91no—
231#443—92no—
232#443—92no—
233#443—91no—
234#443—91no—
235C2×#108—31no—
236C2×#104—92no—
237C2×C4×C8—91no—
238C3×#41—32no—
239C22×C3×C4—31no—
240C2×#67—62no—
241C22×Dic3—61no—
242#239—32no—
243D3×Q8—32no—
244#237—32no—
245#237—62no—
246D3×D4—32no—
247D3×D4—62no—
248#235—32no—
249#235—32no—
250#235—32no—
251#235—32no—
252#235—62no—
253#235—62no—
254#235—62no—
255#235—62no—
256#235C22×D312yes—
257C2×D12—32no—
258C2×C4×D3—62no—
259C2×C4×D3—61no—
260C2×C4×D3—62no—
261C2×C4×D3C22×D311yescharacteristic
262C2×Dic6—32no—
263C3×Q16—31no—
264C3×SD16—32no—
265C3×D8—31no—
266C3×M16—22no—
267C3×M16—32no—
268C3×M16—62no—
269C3×M16—62no—
270C3×M16C22×D312yes—
271C3×M16C22×D312yes—
272C2×C3×C8—21no—
273C2×C3×C8—31no—
274C2×C3×C8—31no—
275C2×C3×C8—31no—
276C2×C3×C8—31no—
277C2×C3×C8—31no—
278C2×C3×C8—31no—
279C2×C3×C8—62no—
280C2×C3×C8—62no—
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D311yescharacteristic
283C3×C42—31no—
284#216—32no—
285#215—32no—
286#214—32no—
287#213—32no—
288C4×Dic3—31no—
289C4×Dic3—31no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3C22×D311yescharacteristic
294#208—62no—
295#208C22×D312yes—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—31no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8C22×D311yescharacteristic
305C2×C3⋊C8C22×D311yescharacteristic
306Dic12—32no—
307Dic12—31no—
308Dic12—31no—
309Dic12—61no—
310Dic12C4×D311yescharacteristic, complemented
311D24—32no—
312D24—31no—
313D24—31no—
314D24—61no—
315D24C4×D311yescharacteristic, complemented
316#204—32no—
317#204—32no—
318#204—32no—
319#204—32no—
320#204—62no—
321#204C4×D312yescomplemented
322ΓL(1,𝔽25)—22no—
323ΓL(1,𝔽25)—22no—
324ΓL(1,𝔽25)—62no—
325ΓL(1,𝔽25)—62no—
326ΓL(1,𝔽25)—62no—
327ΓL(1,𝔽25)—62no—
328ΓL(1,𝔽25)—62no—
329ΓL(1,𝔽25)—122no—
330D3×C8—22no—
331D3×C8—22no—
332D3×C8—31no—
333D3×C8—31no—
334D3×C8—31no—
335D3×C8—31no—
336D3×C8—62no—
337D3×C8—62no—
338D3×C8—62no—
339D3×C8—62no—
340D3×C8—62no—
341D3×C8—122no—
342D3×C8C4×D311yescharacteristic
343D3×C8C4×D311yescharacteristic
344D3×C8C4×D311yescharacteristic
345D3×C8C4×D311yescharacteristic
346C22×C32C2×#4111yescharacteristic
347C2×C3⋊D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3—22no—
350C2×C3×D3C4×D411yescharacteristic
351C2×C3×D3C4×D411yescharacteristic
352D32—44no—
353C32×C4C23×C411yescharacteristic
354C32×C4C22×D411yescharacteristic
355C3⋊Dic3—22no—
356C3⋊Dic3—22no—
357C3×Dic3—22no—
358C3×Dic3—22no—
359C3×Dic3C4×D411yescharacteristic
360C3×Dic3C4×D411yescharacteristic
361C2×#41—92no—
362#135—31no—
363#135—91no—
364#135—92no—
365#135—91no—
366#135—92no—
367#135—91no—
368C2×Q16—91no—
369C2×SD16—92no—
370C2×D8—91no—
371#131—32no—
372#131—92no—
373#131—92no—
374#131—92no—
375#131—182no—
376#131—182no—
377C2×M16—32no—
378C2×M16—182no—
379C22×C8—31no—
380C22×C8—91no—
381C22×C8—182no—
382C2×C42—91no—
383#108—32no—
384#108—31no—
385#108D3211yescharacteristic, complemented
386#104—32no—
387#104—92no—
388#104—92no—
389#104—92no—
390C4×C8—31no—
391C4×C8—91no—
392C4×C8—91no—
393C4×C8—91no—
394C23×C3—31no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3#23911yescharacteristic
398C3×Q8—32no—
399C3×D4—32no—
400C3×D4—62no—
401C2×C3×C4—21no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—61no—
408C2×C3×C4—62no—
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—22no—
412#67—62no—
413#67—62no—
414#67—62no—
415#67—62no—
416#67—62no—
417#67—62no—
418#67—122no—
419C2×Dic3—21no—
420C2×Dic3—62no—
421C2×Dic3—64no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—62no—
425C2×Dic3—121no—
426C2×Dic3#23911yescharacteristic
427D12—32no—
428D12—32no—
429D12—62no—
430D12—62no—
431D12—62no—
432D12C2×C4×D312yes—
433C4×D3—22no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—64no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—122no—
442C4×D3C2×C4×D311yescharacteristic
443C4×D3C2×C4×D311yescharacteristic
444C4×D3D3×D411yescharacteristic
445C4×D3D3×D411yescharacteristic
446Dic6—32no—
447Dic6—32no—
448Dic6—62no—
449Dic6—62no—
450Dic6—62no—
451Dic6C2×C4×D312yes—
452C3×C8—22no—
453C3×C8—22no—
454C3×C8—21no—
455C3×C8—21no—
456C3×C8—31no—
457C3×C8—31no—
458C3×C8—31no—
459C3×C8—31no—
460C3×C8—42no—
461C3×C8—62no—
462C3×C8C2×C4×D311yescharacteristic
463C3×C8C2×C4×D311yescharacteristic
464C3×C8C2×C4×D311yescharacteristic
465C3×C8C2×C4×D311yescharacteristic
466C3⋊C8—22no—
467C3⋊C8—31no—
468C3⋊C8—31no—
469C3⋊C8—31no—
470C3⋊C8—31no—
471C3⋊C8—61no—
472C3⋊C8—61no—
473C3⋊C8C2×C4×D311yescharacteristic
474C3⋊C8C2×C4×D311yescharacteristic
475C3⋊C8D3×D411yescharacteristic
476C3⋊C8D3×D411yescharacteristic
477C2×C32—21no—
478C2×C32C2×C4×D411yescharacteristic
479C3⋊D3—42no—
480C3×D3—21no—
481C3×D3—42no—
482C3×D3#44312yescomplemented
483#41—32no—
484#41—92no—
485#41—92no—
486#41—92no—
487#41—182no—
488#41—182no—
489C2×Q8—92no—
490C2×D4—92no—
491C2×D4—182no—
492C22×C4—31no—
493C22×C4—182no—
494C22×C4—181no—
495Q16—31no—
496Q16—92no—
497Q16—91no—
498SD16—32no—
499SD16—92no—
500SD16—92no—
501SD16—92no—
502D8—31no—
503D8—92no—
504D8—91no—
505M16—32no—
506M16—62no—
507M16—62no—
508M16—182no—
509M16—182no—
510M16—182no—
511M16C2×D3212yes—
512C2×C8—31no—
513C2×C8—31no—
514C2×C8—31no—
515C2×C8—31no—
516C2×C8—31no—
517C2×C8—31no—
518C2×C8—62no—
519C2×C8—62no—
520C2×C8—91no—
521C2×C8—91no—
522C2×C8—91no—
523C2×C8—91no—
524C2×C8—91no—
525C2×C8—182no—
526C2×C8—182no—
527C2×C8—182no—
528C2×C8C2×D3211yescharacteristic
529C42—31no—
530C42—91no—
531C42—181no—
532C22×C3—21no—
533C22×C3—31no—
534C22×C3—31no—
535C22×C3—62no—
536C22×C3—62no—
537C22×C3C2×#23911yescharacteristic
538C22×C3D3×#4111yescharacteristic
539C2×D3—22no—
540C2×D3—22no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—122no—
544C2×D3—124no—
545C2×D3—124no—
546C2×D3#89311yescharacteristic
547C2×D3#89311yescharacteristic
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—31no—
551C3×C4—31no—
552C3×C4—62no—
553C3×C4—62no—
554C3×C4C22×C4×D311yescharacteristic
555C3×C4C22×C4×D311yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C2×D3×D411yescharacteristic
558Dic3—22no—
559Dic3—22no—
560Dic3—62no—
561Dic3—62no—
562Dic3—62no—
563Dic3—62no—
564Dic3—122no—
565Dic3—122no—
566Dic3#89311yescharacteristic
567Dic3#89311yescharacteristic
568C32C2×#44311yescharacteristic, complemented, Sylow
569C23—31no—
570C23—182no—
571Q8—32no—
572Q8—92no—
573Q8—182no—
574D4—32no—
575D4—62no—
576D4—92no—
577D4—182no—
578D4—182no—
579D4—182no—
580D4—182no—
581C2×C4—31no—
582C2×C4—31no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—61no—
587C2×C4—62no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4—182no—
591C2×C4—184no—
592C2×C4—181no—
593C2×C4—182no—
594C2×C4C22×D3211yescharacteristic
595C8—22no—
596C8—31no—
597C8—31no—
598C8—31no—
599C8—31no—
600C8—62no—
601C8—91no—
602C8—91no—
603C8C4×D3211yescharacteristic
604C8C4×D3211yescharacteristic
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—32no—
609C2×C3—41no—
610C2×C3—61no—
611C2×C3—122no—
612C2×C3C2×#89311yescharacteristic
613C2×C3C4×D3×D411yescharacteristic
614D3—21no—
615D3—42no—
616D3—122no—
617D3—122no—
618D3—242no—
619D3#489512yesdirect product factor
620C22—31no—
621C22—31no—
622C22—62no—
623C22—62no—
624C22—182no—
625C22—364no—
626C22D3×#23911yescharacteristic
627C4—31no—
628C4—31no—
629C4—62no—
630C4—62no—
631C4—182no—
632C4—182no—
633C4C2×C4×D3211yescharacteristic
634C4D32×D411yescharacteristic
635C3—21no—
636C3C2×#489511yescharacteristic, complemented
637C3D3×#44311yescharacteristic, complemented
638C2—21no—
639C2—32no—
640C2—61no—
641C2—122no—
642C2—362no—
643C2D3×#89311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radicalD3×#904C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32C2×#443
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D3×#907C2semidirect
3. #10592594C2semidirect
4. C3×#4895C2semidirect
5. C3×D3×#108C2semidirect
6. D3×#825C2semidirect
7. #10590995C2semidirect
8. #10590977C2semidirect
9. #10590919C2semidirect
10. #10590917C2semidirect
11. D3×C8×Dic3C2semidirect
15. #64116C22semidirect
17. C3×#907C22semidirect
23. #63817C22semidirect
24. #63815C22semidirect
26. #63808C4semidirect
27. #63807C4semidirect
28. #63806C4semidirect
31. D3×Dic12C4semidirect
32. D3×D24C4semidirect
33. D3×#204C4semidirect
36. C32×#108C22semidirect
37. #63652C22semidirect
38. C8×C3⋊Dic3C22semidirect
39. C3×#825C22semidirect
40. C3×#822C22semidirect
41. C3×#819C22semidirect
42. C3×C8×Dic3C22semidirect
43. #63570C22semidirect
44. #63568C22semidirect
45. #63553C22semidirect
46. Dic3×C3⋊C8C22semidirect
64. #4895D3direct (N × H)
65. D3×#108D3semidirect
86. #3746C2×C4semidirect
87. #3745C2×C4semidirect
88. #3744C2×C4semidirect
95. C3×Dic12C2×C4semidirect
96. C3×D24C2×C4semidirect
97. C3×#204C2×C4semidirect
107. #3719C2×C4semidirect
108. #3717C2×C4semidirect
109. #3716C2×C4semidirect
110. #3714C2×C4semidirect
144. #907C2×D3semidirect
169. C3×#108C2×D3semidirect
170. C3×#108C2×D3semidirect
179. #825C2×D3semidirect
180. #822C2×D3semidirect
181. #819C2×D3semidirect
188. C8×Dic3C2×D3semidirect
310. Dic12C4×D3semidirect
315. D24C4×D3semidirect
321. #204C4×D3semidirect
385. #108D32semidirect
482. C3×D3#443semidirect
568. C32C2×#443semidirect
619. D3#4895direct (N × H)
636. C3C2×#4895semidirect
637. C3D3×#443semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D3×#9072
D3×#9042
#105925942
C3×#48952
C3×D3×#1082
D3×#8252
#105909952
#105909772
#105909192
#105909172
D3×C8×Dic32
D3×#4433
C2×#48953